Te.
FTD-MT-24-135-69-Vol I of IL
FOREIGN TECHNOLOGY DIVISION
AD695929
LIQUID FUEL ROCKET ENGINES — DESIGN FUNDAMENTALS
Wistribution of this document Is unlimited. It may be released to the Clearinghouse, Department of Commerce, for sale to the general oublic.
Reproduced by the CLEARINGHOUSE for Federal Scientific & Technical Information Springfield Va. 22151
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sit
FID-MIT- 24-135-69-Vol 1 of II
EDITED MACHINE TRANSLATION
LIQUID FUEL ROCKET ENGINES — DESIGN FUNDAMENTALS By: M. V. Dobrovol'skiy
English pages: Cover to 301
Source: Zhidkostnyye Raketnyye Dvigateli. Osnovy Proyektirovaniya Moskva,
: . '
Izdatel'stvo "Mashinostroyeniye,'
1968, pp. 1-396.
THIS TRANSLATION IS 4 REMDIVION OF THE ORIGL- MAL FOREIGN TEXT WITHOUT ANY 4MAL YTICAL OF
EDITORIAL COMMENT. STATEMENTS OR THEORIES PREPARED BY, ADVOCATED OR MPL/ED ARE THOSE OF THE SOURCE
AND DO MOT WECESSARILY REPLECT THE POSITION TRAMSLATION ФГУ:
OR OPINION OF THE FOREIGN TECHMOLOGY 0+ POREIGH TECHNOLOGY Division У. УР-АРВ, ОМЮ.
ЕТО-МТ- 24-135-69-Vol I of II Dew 27 June 19 69
C1-ACCESHOM MO. 98-DOCUNENT Loc
TM9500997
@.T1T
"6 LIQUID FUEL ROCKET ENGINES-DESIGN FUNDAMENTALS
A LTE NMEA пиво есче ити < | DATA HANDLING PAGE
TOPIC Tacs
spacecraft propulsion equipment, liquid propellant engine, nozzle flow, combustion chamber, liquid rocket fuel, combustion kinetics, fuel injector
47-SUBJECT AREA
21
9 -АиТмОй/Со-лиТнОй$
DOBROVOL'SKIY, M. V,
1O-DATE OF INFO
43-SOURCE
ZHIDKOSTNYYE RAKETNYYE DVIGATELLI. OSNOVY PROYEKTIROVANIYA (RUSSIAN) 60401 63-SECURITY AND DOUNGRADING | HFORMATI On 64-CONTROL MARKINGS |97-HEADER C\ ain UNCL, O NONE UNCL 7e-REEL FRAME WO. |77-SUPERSEDES 78-CHANGES -eeoenapmi ca WO OF PAGES a 1889 0850 UR 615 CONTRACT NO. x REP Acc. MO. PUGLI SMING DATE TyPa PRODUCT REVISION PREG 65- 94-00 TRANSLATION NOME he но 02-UR/0000 68/000/000/0001/0396 ——"—
АВУТИАСТ
given.
fuels and materials and t foreign and domestic public methodical and do not pertain book is a textbook for students o and can also be useful to engineers
wee
engines (ZhRD). chamber and the propulsion system on the whole, of the theory, methods of calculation and description of sub- assemblies and «nits of devices with liquid fuel rocket engine are Processes of expansion of gases in nozzles, carburetion
and heat exchange are expounded, as well methods of profiling nozzles, calculation of injectors, determination of forms and volumes of
An analysis of work of installations with Supply systems with turbopump
combustion chambers, h open and closed circuits is given, assemblies ard pressure feed systems with gas, powder, and liquid pressure generators are considered, work of installations with closed circuits and methods of power coordination of such circuits, were given, in particular, a description of the propulsion system of the rocket "Vostok."/{/The book gives actual data on structures, r characteristics on the basis of
Examples of designs are purely
ons,
(U) Thie book presents design fundamentals of liquid fuel rocket It considers questions of design of the engine Basic statements
Much attention is allotted to
Examples of propulsion systems
any defined type of engine. igher educational institutions graduate students specializ-
The
TABLE OF CONTENTS
U. S. Board on Geographic Names Transliteration System
хофоефоооео Vv
зооооооофооо ооо овоо vi
Designations of the Trigonometric Functions
List Of ACTONYMS se eee sees eeeceeceeeenseeccce,
OCH ee men eter neee vil
Preface........,
ie в 1х
Chapter I. General Remarks
a 1
В. Classification of СН" Fuel.
ca rn 1
1.2. Basic Parameters of ZhRD
a 12
1.3. Systems of Loss Coefficients, Expenditure of Fuel and Basic Dimensions of Nozzles
i ee a 20
Chapter II. Nozzles of a Liquid Fuel Rocket Engine............ 26 2.1. Types of Nozzles and Basic Requirements of Them..., 26
2.2. Losses in the Nozzle of a Liquid Fuel Rocket Engine.........
a 29
2.3. Designing of Conical NOZZLES eee cece cece eee 42
2.4. Basic Initial Positions in the Construction of a Profiled №0221е........,....
оооооооров ооо ооо оовово 43
2.5. Shortened and Optimum Nozzles
ооо ко овововне 48
2.6. Approximate Method of Construction of a Contour of an Optimum №221е.,......
ооо ооо ооо ооо о вос 24
2.7. Operation of the Nozzle in Off-Design Conditions
with High Counterpressure,
he ere 60
2.8. Work and Characteristic of Nozzles with a Central Воду...............
a 64
i 2.9. Calculation of Nozzles with a Central Воду......... 73
Chapter III. Carburetor and Chamber Heads of ZARD.......0..64. 86
3.1. Basic Elements of Carburetion and Combustion Processes
иво н иво во ооюоооввоюонь.. = 86
D2 Spray INJOCEOTS. eee eee ee eseeeeees ease cn, 102
—— ЧЩ
3.3. Centrifugal ИИ 112
2.4. Тио-Сотропеп+ Injectors
i rn 132
FTD-MT-24-135-69 1 ad ila
|
3.5. Chamber Heads for %Пе 218О.........ъъьзееооновеоов о
3.6. Influence of the Hea’ on Carburetion and Specific
АЦ. с. а oe cc ees ce ene ee we etele ceclls po cece.
Chapter IV. Cooling of CORD. ccccccvcccvevccsvtsescevessesevece
4.1 Heat Exchange in ZNORD,. . crcvcovcvcccvccccvsceseceeees
4.2, Methods of Cooling the ZNRD.....cceeccccsevcencvene
4.3. Process of Convection Heat Transfer from the Gas to
the ШИ со ооо oleic Ио в о ИИ, ИИ И...
4.4. Internal Reiations of Energy and Impulses for the
Boundary Тауег......озовюововоь ооо обо воен совоноосо
4.5. Solution cf the Integral Relation of Energy.......
4.6. Calculation of Convection Heat Exchange in a
РОВ нь Зе о оо оба о еее о о бед о ве В «о вла в
4.7. Conversion of Convection Thermal FlowS...cscecceees 4.8. Determination of Radiant Heat FlowS....cccceccscese
4.9, Determination of Heat Transfer from the Wall to the Cooling Liquid......
4,40, Forms of Coolant Passages of Chambers of a
ПЕ, оо Мер т Зе ое те РВ. ЕСМ. ве we ae
4.11. Calculation of Heat Transfer in a Ribbed Coolant.
Passa Зсезевоео ооо оо ооо ово ово ооо оо воре ооо воосово
4.12. Calculation of Cooling of a ZNRD, ооо ооо оо ооо 4.43. Certain Special Cases of Cooling ZNRD... cece eee eee Chapter V. Chambers of Liquid Propellant Rocket Engines.......
в... Shapes and Examples of Existing Chambers of Liquid
Propellant Rocket ENZineS...cocccccvcccvevrscvscesene
5.2. Determining the Volume of the Combustion Chamber...
5.9. Unstable Burning. .cccscvcccccccvccvsvecesvescescesese
5.4. Start and Shutdown of Engine... ..cscccccsesvecececs
5.5. Aftereffect Impulse......ccccsoes
5.6. Engine Chamber Strength Calculation.......
eeoeeeseeeeoeeeeoesveen
5.7. Additional Ветагк$.......ъьзовоовоооооововеовосово
FTD-MT-24-135-69
11
137
Lis, 165 165 174
137
196 212
220 225 238
248
302 310 214 221 329 336 342
Chapter УТ, Propulsion SYStOMS cece eee c eee ceccecaesececevce, 345
6.1. Feed И 345
6.2. Propulsion Systems with a Turbopump Feeding SUPERS ани ое аа, 348
6.3. Thrust and Specific Thrust of a Propulsion А ЗУМ ии ие рь и иконе озненианинннь 358
6.4. Fuel TANKS .. cc ceccceccecee.
оооооовово ооо ооо ооо вое 361
6.5. Feed System EQUIPMENt eee eck eee eeeeecees cece, 370
6.6. Determination of Feed Pressure and Hydraulic } Characteristics of the Feed SYStOM. . ccc eecccccecee. 381
6.7. Systems of Control and Adjustment of a ZORD........ 388
6.8. Examples of Systems Carried Out with Turbopump | Feed
FETS O08 SMe eithe ° Sisie Wes 0 069 0% Fis e Org ons 9 ohare tL 397
Chapter VII, Turbopump 9168... оон рооонозавичень, 412 7.1. Pumps for Feeding Components to BARD... . ewbev cee ia 413
7.2. Calculation and Characteristics of ZhRD Pumps....., 433 7.3. TNA Turbines
ооо ооо носов о оо о ооо вево ооо 446
7.4, Joint Operation of Turbine and 0) ньньь 465
7.5. Gas Generators
i rn 479
Chapter VIII. Closed-Circuit Propulsion SYSCEMS ..... eee eee ees 496 8.1. "Gas + Liquid" Closed CLVCULE. eee eee cece ee eueee 498
8.2. Closed "Gas + Liquid" Circuit without 2160......... 544
8.3. Closed "Gas + Gas" Circuit
ооо во оо ооо воово сос ое 520
Chapter Ix, Propulsion Systems with a Pressurized Feed еде,
ооо ооо ооо бов ооо ооо ово ооо 525
h 9.1. Gas Cylinder Feed SYStCM ине ююневивань, 527
9.2. Ехатр1ез ог Propulsion Systems with Gas- ‘ Pressurized Feed...
re ee re 537
9.3. Reduction Valves of Gas PrESSUTE... ии... ,., 547 9.4, Characteristics of Reduction VALVES... eee eee eeeee, 554
9.5. Design of Reducing Valve
ооо ово ооо ооо ово ооо 570 РТР -МТ-24-135-69 111
= ACL ea
9,6, Displacement Sup 7ТПАО, с. .озаоеье
9.7. Propulsion Syste Hybrid Engines [
Аррепаех. „ии иене нение ниве ee
Вал овгарпу нение ково ие вет
FTD MT-24-135-69
ply Systems with PAD and
ms with Preliminary Fueling and 149[, [150], [151]. ce vecceseneccers
iv
519
295 601
605
U. S. BOARD ON GEOGRAPHIC NAMES TRANSLITERATION SYSTEM
Block Italic Transliteration Block Italic Transliteration Aa Aa A, a РР Р р В, г
B 6 B 6 B, b С с С ес 8, в
В в Be У, у Тт T m т, ©
rer re G, Е ух yy U,u
Да Zé р, а o @ ФФ F, f Ee Ес уе, уе; Е, е X x Хх Kh, kh Жж MM 121, th Цц Ц у Ts, ts 8s 3. 2, $ Ч + Ч ч Ch, ch Hon И и I, i Шш Шш Sh, sh AA Aa У, у Щш ЦЩЦым Sheh, shch K & Кк К, К b > Sb 3 п
Ла Ла L, 1 Ыы HW ow У, у
Ми Ми М, м ьь ь ь '
Ни Hon М, п Дэ. ду Е, е
Оо 0e 0, о Ю»ю Ю» Yu, yu Па Пя Р, р Я я Aa Ya, ya
* te initially, after vowels, and after 4, b3 e@ elsewhere, en written as # in Russian, transliterate as y¥ or ¥, The use of diacritical marks is preferred, but such marks may be omitted when expediency dictates.
РТО-МТ-24-135-69 у
— bo oul = TS Янин а a. № едеимный ее — ет Г
FOLLOWING ARE THE CORRESPONDING RUSSIAN AND ENGLISH DESIGNATIONS OF THE TRIGONOMETRIC FUNCTIONS
Russian English ain sin cos cos tg tan ctg cot sec sec cosec csc sh sinh ch cosh th tanh cth coth ach sech csch esch ere sin 8111 arc cos cos~) arc tg tan71 arc ctg cot~) arc sec вес-1 arc cosec свс-1 are eh sinh71 are ch cosh™2 arc th tanh~) arc cth coth=2 arc ach sech™1 arc csch cach) rot curl lg log
| PTD=MT~24-135~-69 vi
о и
heey
List of Acronyms
Following is a list of conventional acronyms utilized in the
translation of this document.
ВАОР (БРДД) — long range ballistic missile EPK (SPH) — electropneumatic valve
GRD (TPA) — hybrid engine
Lif (English only) — lunar module
LPRE (English only) — liquid fuel rocket engine NDMG (HOMT) - nonsymmetric dimethylhydrazine PAD (MAX) — powder pressure accumulator
PGG (NTT) — steam-gas generator
RDTT (PATT) — solid propellant rocket notor SAS (CAC) — emergency rescue system
TNA (THA) — turbopump assembly
VRD (BPO) — jet engine
ZhAD (HAD) — liquid fuel pressure accumulator ZhGG (HIT) ~— liquid-gas generator
ZhRD (HPQ) — liquid fuel rocket engine
ZUR (3YP) — SAM
FTD=-MT-24-135-69 vii
la Bld a AS alii GAMES ARA ca A AR ei A an es me
ре т oR Pete AN AY
‘A, ЕАМ ma |
This book presents design fundamentals of liquid fuel rocket engines (ZhRD). We consider questions of design of the engine chamber and the propulsion system on the whole. Basic statements of the theory, methods of calculation and description of subassemblies and units of devices with liquid fuel rocket engine are given.
Processes of expansion of gases in nozzles, ecarburetion and heat exchange are expounded, as well methods of profiling nozzles, calculation of injectors, determination of forms and volumes of combustion chambers. An analysis of work of installations with open and closed circuits is given. Supply systems with turbopumo assemblies and pressure feed systems with gas, powder, and liquid pressure generators are considered.
Much attention is allotted to work of installations ‘with closed circuits and methods of power coordination of such circuits. Examples of propulsion systems were given, in particular, a description of the propulsion system of the rocket "Vostok."
The book gives actual data on structures, fuels and materials and their characteristics on the basis of foreign and domestic publica- tions. Examples of designs are purely methodical and do not pertain to any defined type of engine.
The book is a textbook for students of higher educational institutions and can also be useful to engineers and graduate students specializing in rocket technology.
FTD-MT-24-135-69 viii
PREFACE
More than ten years have passed since the first Soviet artificial earth satellite opened the era of conquest of outer space. The most important elements in space rocket systems are propulsion systems with liquid fuel rocket engines (ZhRD) which ensures only flights at earlier unattainable velocities within limits of earth's atmosphere, but also the possibility of flight in outer space. The apparent simplicity of ZhRD, the very idea of which was expressed by K. E. Tsiolkovskiy over 70 years ago, the creation of such engines has required knowledge and experience corresponding to the present level of science and technology, wide introduction
of methods of hydrodynamics, gas dynamics and heat exchange to engineering designs.
A contemporary propulsion system with a ZhRD constitutes a complicated system, the work of subassemblies and units of which 13 interconnected. Therefore, design of one or another unit is impossible to conduct separately, neglecting the construction and work of remaining elements of the installation, which creates definite difficulties in the presentation of corresponding material.
In the present textbook we have attempted a systematic account of design fundamentals of chambers of the engine and the propulsion system on the whole. By contents it is possible to divide the book into two parts: Chapters I-V, which expound basic questions of design of engine chambers, and Chapters VI-IX, which examine basic questions of design of the propulsion system on the whole.
FTD-MT-24-135-69 ix
<—s
врали jr twmmata cet ett ne nfo stearate Da Nara: ARERR rene
It is assumed that students in the present course are familiar with fundamentals of rocket technology and the theory of working processes in ZhRD. However, for convenience the first chapter presents briefly the basic ideas which are used in examining the various questions in designing 2180. For a best understanding of working processes and peculiarities of design of elements of these engines the basic design methods are illustrated by examples.
In view of the limited volume of this book, certain questions (turbopump assemblies, control, etc.), examined in special textbooks or aids are given in compressed form. Moreover, only the basic information necessary for a correct approach to designing installations on the whole are given. The author has tried to avoid mathematical computations in cases when they cannot be used for a direct calculation of the various elements of a propulsion system.
When writing the textbook we systematized information published in periodicals and books and also made use of earlier published works of the author.
We express our deep gratitude to Professors S. D. Grishin, F. L. Yakaytis, and Docent Yu. V. Krylov for valuable remarks and recommendations made in reviewing the book, and also Professor
G. B. Sinyarev for his valuable advice, given during a joint discussion of the book.
The author requests that readers send their opinions and critical remarks to the following address: Moskva, K-51, Petrovka, 24,
Izdatel'stvo "Mashinostroyeniye" [Mocksa, K-51, Merposxa, 24, издательство "Машиностроение ]."
РТО-МТ-24-135-69 х
CHAPTER f GENERAL REMARKS
The present chapter gives basic ideas and relationship between Parameters which must be known for Studying desig¢n fundamentais of ZhRD. Moreover, it 1s assumed that the reader is acquainted with fundamentals of rocket technology and the theory of working Processes In chambers of ZhRD, in consequence of which ideas and relationships to be mentioned later are given in concise form without Proof. Those who are interested can find ereater detail on proofs and analysis of these relationships in works '25], [14], апа [2].
deals Classification of ZhRD Fuel
Liquid-propellant rocket engine is the name of rocket engines which use liquid fuel.
Liquid fuel and liquid oxidizer move from tanks to the engine chamber where, as а result of fuel combustion, high-temperature Gaseous products are formed (Fig. 1.1). In the nozzle they are expanded from the chamber pressure to the nozzle section pressure and flow into the Surrounding air at high speed. The outflow of
Gases from the nozzle is the cause of the reactive force of the engine,
PTD-¥T=24-1 35-69 1
Pig. 1.1. iagram and cycle of ZhRD.
Classification of ZhRD
The type of ZhRD is determined by some characteristic criterion (fuel, circuit, method of suprly, assignment, etc.). Figure 1.2 gives a diagram of classification of ZhRD in terms of basic charac- teristic criteria. Work of ZhRD with the different circuits, methods of supply, structural elements, conditions of operation and also basic properties and types of fuels used are explainea in subsequent sections of the book. Therefore we will not describe a given circuit in terms of noted criteria. Let us consider oniy the area of application of ZhRD.
Area of Application of ZhRD
The basic application of ZhRD is as the engine of rockets, whence the name liguid propellant rocket engines.
They are the basic type of engine of launch rockets of satellites or spaceships. Figure 1.3 shows the three-stage rocket "Vostok," which was used for orbiting the spaceship with astronaut Yu. A. Gagarin. Figure 4.29 shows the propulsion system of the first stage of "Vostok" liquid propellant rocket engine RD-107. Figure 6.7 shows liquid propellant rocket engine "Cosmos" RD-119 for the second stage of "Cosmos" rockets launch. Figure 1.4 shows a dtugram of the three-stage launch rocket "Saturn-V" with the "Apollo" intended for flight to the moon. Thrust of the propulsion svstem ot the first stage is 3400 t (13.4 MN). Figure 6.32 gives an ansembiy diagram of the propulsion system of the first stage of vne launch rocket.
PYD-M 2-241 35-69 2
pee este
oxyzen
Py Nitric acid oxidizer Hydrogen peroxide ] Iwo- a Fluoride, - Component Ее. ГАНуа горит peroxide | courant Няни Е eto. With open ву cireuit | cireuit With closed — By means circuit apor from у > -| woeling systen | Ж = medium apping gaa roine pump haaber р ky supply Г etc. _ ayst oe Ц Displacement aa A `
Ballistic rocket
» Weather rocket
By operational | conditions
Ry construction of separate elements
Fig. 1.2. Classification of ZhRD.
FTD-MT=24-135-69 3
[Pultichamber — |
Ц замы зы
Fig. 1.3. "Vostok."
5 /
fe" ‘
Liquid fuel rocket engines are widely used in long-range ballistic missiles (BRDD) and those of medium range of operation, ABM, SAM, and 2110 in metecrological rockets. Figure 6.31 shows the assembiy 3° a-rarm of the propulsion system of the "Atlas" BRDD.
Liquid fue! rocket engines are also one of the basic types of chgine utilized in spaceships for braking and in orientation system (Fig. 1.4). Fisure 9.6 shows a diagram of an installation for vorreci ing tue speed of a spaceship.
an tars tm si actigiin ined
Fig. 1.4. Diagram of "Saturn" launch rocket with "Apollo" and emergency rescue system (SAS): 1 = first Stage; 2 - adapter becween first and second stages; 3 — second Stage; 4 — adapter between second and third stages; 5 — third stage; 6 — instrument Section; 7 - LM; 8 — engine section; 9 — "Apollo" command module; 10 — SAS; 1l — crew section; 12 — adapter between launch rocket and Spaceship.
Besides use in rocket Systems, ZhRD have found application as the engine of other than rocket systems. Liquid fuel rocket engines are set on aircraft as a basic engine as well as for start boosters
(Fig. 1.6). They are also known to be used as the engine of torpedoes.
8 Ge
Fig. 1.5. ZhRD for orientation system: a) 90 kg {883 N) thrust; b) 7.2 ke (70.6 N) thrust.
Fig. 1.6. Kbei-Kns ai
Jn contrast to us fuel, in Z2hnRD
For @ ei
Fuel
the fuel is oxidizer
rerall atecavciauui.
ual thermal machines where fuel is actually
+ fuel.
yen oxidizer and fuel, properties cf the fuel are
ermined by their relationship, which is characterized by
excess Gxiduit ratio
ге , anv uo
У
oo Yo
— stoteniometrical and real ratio of expenditure
6
‘ sxiGises to expended combustibie respectively. Value a essentially
“sote the pasie propellant properties.
In ZhRD we distinguish fuel which is Spontaneously inflammable,
1.e., inflammable upon contact of oxidizer with fuel, and
non-self-igniting, 1.e., requiring an outside source of ignition.
We also distinguish two~=compenent and single-component (unitary ) fuels.
Liquid fuel rocket engines almost exclusively are bi-propellants. Monopropellants are used mainly to drive to turbopump assemblies (TNA) (in systems with PGG) and in certain low thrust engines [for example, engines of orientation Systems of spaceships (see Fig. 9.1)].
According to conditions of exploitation fuels are divided into high-boiling and low-boiling (cryogenic) fuels, the components of which under norma] conditions are liquified gases (for example, oxygen, hydrogen, fluorine).
Requirements on fuels of ZhRD can be divided into three groups: a) basic, b) Structural, c) operational.
Basic requirements are determined by the main problem — obtaining the greatest specific thrust with the smallest possible mass of the propulsion system. Finally they are formulated зо: the fuel should possess a large reserve of chemical energy and high density, and combustion products of the fuel should possess good thermodynamic Properties (value of as constant, isentrope index, etc.).
Structural and operational requirements are determined by the problem of Creating a propulsion System which is reliable, convenient in operation, and as cheap as possible. In accordance with these requirements one evaluates the physical properties of the fuel, cooling properties, ability to self-ignite and limits of inflammability, chemical stability, explosiveness, aggressiveness with respect to metals, toxicity, boiling point and fusion point, and, finally, cost of the fuel.
Thus, components of fuel have numerous and various requirements which Simultaneously can not be satisfied by one of the components,
although the possibility of use in fuels of almost all elements of the periodic system of Mendeleyev has been investigated [23].
In ZhRD the basic components of fuels are oxidizers on the basis of oxygen (pure oxygen or its compounds) and fuels on the basis of hydrogen and carbon (hydrocarbons, hydrazoic compounds, pure hydrogen). In the very near future it is possible to expect the use of fluorine and its compounds as oxidizer and compounds of boron, beryllium, and lithium as fuels.
Tables 1.1, 1.2, and 1.3 give certain basic properties of oxidizers, combustibles, and fuels.
Table 1.1. Basic physicochemical properties of certain oxidizers used in liquid fuel rocket
engines. i 1 full heat content % 3 | & : Я 016430 | | 8 . 1 < Е sf } 7 3 $ 2 ase i Фа: 2 м м 8 we |e $3. Кут, 11914 O, | 22 ид —3100 |—402 | 1140 | 54,3" и 0.1! Pluorine, liquid Fy —3000 1—3 |150 | 55.16] 85, 1613.2 №4716 2014 f —4140& ‚—2780 | 1510 |231 5/359, 16] 0,28 таг. Ozone | +3020 |+-2635 | 1700 | 21,761161,66] ~. Fluorine monooxride +2060 [+222 | 1820} 49 | 128, — water 18,01 ram —68370 |—15880) 1000 a a a
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11
1.2. Basic Parameters of ZhRD
Here and below the parameters related to the chamber of ZhRD will be designated in accordance with flow of the cycle of a ZhRD and characteristic sections (see Fig. 1.1). We will relate all parameters of a combustion chamber to section "2," 1.e., pressure in the combustion chamber, temperature, density, etc., will be
designated Po; Т›; Po, etc. In cases when we consider acceleration of gas in the chamber, we will use parameters of braked flow.
Thrust and Specific Thrust
Thrust and specific thrust are important parameters of ZhHRD. The formula for thrust traction assuming one-dimensional flow of gas through tne nozzle of ZhRD has the form
Ра р), (1.1)
where P — thrust; G — fuel consumption; P33 W33 Г} — pressure, speed, and area of cross section on nozzle section; p, — ambient pressure.
When Рз = Рн the engine works in design conditions so design thrust
Р.А С. (1.2) e If Рн © 0, 1.e., when the engine works in a vacuum, thrust in a vacuum РТО (1.3)
When P3 > P, or Pz > Py of the engine works in conditions of under-
expansion and overexpansion respectively.
Specific thrust, i.e., thrust referred to flow rate per second of fuel
р Ри
[уд -— specific]
12
or
Py m+ B(p,—p). (1.4) In design conditions Paw, (1.5)
Pint, (1.6) 8 where w= 0, +A (p,— д. (1.7)
ZhRD since on its value, in the end, depends the loading factor
of the rocket System (ratio of payload to Starting load) Figure 1.7 gives a calculation graph of change of initial mass of System for launching satellite with a mass of 5 io? & depending on specific thrust.
бы 7
Fig. 1.7. Influence Of specific thrust on initial mass of the System.
м КГМА
м № : ни ны у 2 Би чи ьм:
In heat engines one frequently meets the idea of Specific fuel
consumption, i.e., fuel consumption per unit of time for a thrust of 1 kgf.
Gp Pom me AF (1.8)
13
Inasmuch as specific consumption in ZhRD is simply connected with specific thrust, the concept of буд is rarely used.
Basic Relationships of ZhRD
The basic relationships characterizing work of ZhRD and defining its characteristics are: specific impulse 8, thrust coefficients K and K, and expansion ratio of the nozzle £3/fup: (Kp - critical].
Specific impulse 8 (or complex 8) of pressure in a combustion chamber 15
p= er (1.9)
If one were to express 6 as the ratio of fy p, vo mass flow rate,
then 8 has the dimension of speed ms. Therefore in Western literature specific impulse is usually called characteristic speed and is designated by c*.
The theoretical value of 6 is calculated by the expression obtained from the equation of consumption
pa BE (1.10)
Неге
аут, (1.11)
n — polytropic index of expansion of combustion products from Po to
Pxp .
Values “RAT, and AL depend on the kind of fuel and barely depend on other parameters of work of an engine (within limits of 1-2%). Therefore we approximately consider that theoretically ® depends only on the kind of fuel and is a constant thermodynamic characteristic of a given fuel. For a given fuel the value of the 8 complex depends only on the qualitv of the flow of processes
14
in the combustion chamber and does not depend on processes in the с. Thus, for a given fuel & is a characteristic determining the
.
work of only the combustion chamber. Nozzle thrust coefficient K (or thrust coefficient )
К--Р.. (1.12) SapPr The thrust coefficient shows how many times engine thrust exceeds the basic component force of thrust fy. p.- Therefore, sometimes К ts ealled dimensionless thrust. The theoretical value of K is
‘alcuiated by the expression obtained from the formula of thrust
(1.13)
where mn. — mean index of Isentrope of expansion. It is more
convenlent to use the thrust coefficlent in a vacuum K :
K,=—., (1.14)
SupP2
When p, * 0 the calculation expresston for K is obtained from equation (1.13):
ae
fas т Г a and | =)“ у '- (=) eX x] 14 Sect Е
1 „1 Г ~ er (1.15)
le Pa _|
As we sce, K. does not depend either on work of the combustion chamber
or cn external conditions (ps) and is a characteristic determining
work of the nozzle of the chamber only.
In accordance with formulas (1.1) and (1.3) K and K.. are
connected by k=k,-£ ©, (1.16)
whence taking into account equality (1.12) we obtain the expression for determination of empiricai
К... = P= FaPa
(1.17; Л upP2 :
where P. — measured rea! thrust of engine. Comparing expressions (1.9), (1.12) and (1.14), we obtain the formula fcr determination P and P ГЕ
Py=3K; Py,,=3K,. (1.18)
Expansion ratio of the nozzie Г. (or simply broadening) is defined as the ratic
я (1.19)
| This value not only determines nozzle dimensions but also characterizes basic parameters of work of the nozzle p3/p3> М. (ог зрееа из) › B70 3- (Here and below the asterisks "#"" designate parameters of braked flow).
(1.20)
16
”
me
А
еее, (1922) --у == 2, er 1-2) * |. (1.22)
"as tee (1.23) т = Ag —! 2, Е (1.24) Е т Е - (1.25)
Comparing resulting expression, we see that broadening of the nozzle is simply defined by any of the basic parameters of work
of a nozzle. Relation
ё-. 3 ‚ (1.26) Pe Е
is called the expansion area ratio of a nozzle. As we see from
а. (1.20), expansion ratio 6 for an assigned fuel, (.е.. _) and broadening of the nozzle Г: do not depend on a change of pressure in the combustion chamber.
Relationships (1.20)-(1.25) are obviously valid not only for @etermination of parameters on tne uozzie section, but also permit determining р%/р› M (or w), р%/р in any section of the nozzle with f= f/T.,..- Using the shown relationships, one can determine the change in p, w, р, T cver the iength of the nozzle. Figure i.8 gives a graph of the change of broadening depending on ratio p5/p and the isentrope of expansion n .
17
Fig. 1.8. Dependence f/f... =
(а...)
Characteristics of ZhRD
In ZhRD we distinguish two basie types of characteristics: throttle and altitude.
The throttle (or consumption) characteristic is the name of the dependence of thrust P or specific thrust Руд on consumption of eomponents G at constant altitude.
The altitude characteristic is the name of the change in thrust P or specifie thrust P_. depending on altitude of work cf the engine H (or an ambient pressure p_) during constant consumption.
The equation of the throttle characteristic P = f(G) is obtained trom the formula of thrust (1.1) converted taking into account relationships (1.9) and (1.26) and taking p, = p§:
Pu=G (2+ м (1.27)
fnasmuch as the sum in parentheses and member f 32; do not depend on ‘onsumption, the equation of the characteristic has the form of an tquntion of a straight line
P=AG-B.
‚ 1. 1.Ya are represented throttle characteristics plotted from equation (1.27) for an engine with different expansion ratio, and
18
ath a eth
as NAN
on Fie. 1.9b for an engine working on lana (P.. = Ро) ana ina vacuum {P. = 0). [Г there is a considerable decrease of
sonsumption as compared to eulculation conditions separation of flow from walis of the nozzle will occur (see section 2.7). т this case equation (1.27) will not be valid and the real characteris-—
tic will го through the origin of coordinates as shown by the dotted
го
Ly | е) рь=0 г
Siz. 1.9. Characteristics of 2580: а, b) throttle characteristic of thrust (P = f(G); с, 4) throttie characteristic of specific thrust (P = £(G))3; e, f) altitude
characteristic.
The throttle characteristic of change of specific thrust is obtained from formula (1.27):
— 3 1 Fs 94 ЛР т =. (1.28)
39
During work of the engine in a vacuum (P,, = 0) Patt 83, (1.29)
4.е., зрес1Г1с thrust in a vacuum does not depend on consumption.
On Fig. 1.9c, d are shown throttle characteristics P= f(3) and P.. = £(S) for engines with different expansion ratios and
улей
for engines working at various aititudes.
Dependences of thrust or specific thrust on flight altitudes (altitude characteristic) are determined directly by formulas (1.1) or (1.4), in which with a change of height only p,, 1s changed. From a comparison of these formulas it Is clear that the character-= istic of thrust and specifie thrust differ in altitude only by scale (Fig. 1.9f). The altitude characteristic of thrust or specific thrust in terms of aititude of work for engines with different
broadenings are shown In Fig. 1.9e.
Systems of Loss Coefficients. Expenditure of
$3. imensions of Nozzles
System of Coefficients for Evaluating the Quality of Processes in ZhRD
For evaluating the quality of flow of processes in ZhRD it is possible to use either efficiencies, which estimate the perfection of conversion of initial energy into effective work, or coefficients, which estimate the loss of specific thrust (impulse) due to a low- quality flow of processes of conversion of energy.
in the first case there will be the so-called power coefficients (efficiency), in the second, impulse coefficients.
In ZhRD the more commonly used are impuise coefficients, examined below. Power coefficients are detailed in [14] and [25].
If one were to designate ¢ on the loss factor of specific
thrust then specific real thrust could be defined as
- 30) Риа=Р'. (1.3
be
losses of specific thrust in general are determined by losses in
tA "5
the chamber, in the nozzle and on thermal resistance, which we will estimate accordingly loss factor in the chamber ¢,, nozzl2 coefficient
and loss faectcr on thermal resistance $ п? 30 that
P= FaPcPremr (1533)
Above we noted two basic parameters, determining processes in a combustion chamber and in a nozzle: complex & and K.. The distinc- al value of complex § , obtained on the basis of
a
experimenta ata by formula (1.9) from the value calculated by equation (1.10)
flow of processes in the combustion chamber, 1.e., losses in the
combustion chamber (for detail see section 3.6). Thus .-®. (1.32)
If, durinz a comparison of calculation and real values or complex 8, real expenditure is set equal to ealculation and the calculation of 8 is conducted at real value Pry» 3.е., Gi. = G and i =f , then
и
fie. 5;
' A Thus, $, characterizes the value of losses of pressure due to the low-quality of processes. Therefore ¢, is frequently called the
coefficient of fullness of pressure. ~
Placing in equation (1.32) the value of 8 from formula (1.10), we obtain
_WRTs
Фи Уят. *
21
whence, taking R.,.. = Ros
Та — (1.34) т. %
Formula (1.34) permits for known or assigned 6, approximately estimating the decrease in design temperature in the combustion
chamber due to losses in it.
Losses in the chamber are made up cf two forms of losses: losses on incompleteness of combusticn due +$с the low-quality flow of processes of conversion of fuel into combustion products (see section 3.1) these losses do not yield to exact calculation, are usually determined experimentally, and are characterized by the coefficient cf incompleteness of combustion 9. ‚г)з апа losses on rregularity of distribution over the section of the chamber of the ratio of components and specific weight flow, expressed by variation factor $.,- Thus,
es ‘л Ne
$ = Ferra (1.
Total losses in the combustion chamber are within limits Фи = 0.95- 0.99.
Losses in the nozzle are defined as the ratio of the real value of the thrust coefficient in a vacuum K, д defined on the basis of results of experimental data by а (4547), to its theoretical value calculated by formula (1.15):
a=. (1. 36) In general they are composed on losses on dispersion of flow
(Фрас )» on friction (9), inlet (¢.,)2 on nonequilibrium of the process of expansion (Gi. I» on nonadiabaticness (Фохл )› and also of losses connected with the presence of a boundary layer ($... уж)» and losses during expansion of a two-phase flow (op )- Thus,
Зе рес Р:р Pan teepTezatcy a2: (1.37)
22
REE
e.
Losses on thermal resistance take place only in a high-speed combustion chamber. Then calculation is given in works [2] and [110]. ic combustion chamber ¢.,.., = 1, and then expression
3? = ФТ». (1. 38 ) Determination of Fuel Consumption and Areas of Nozzle Sections f,, and РГ. =} 3 Let us examine now we determine taking losses into account,
fuel consumption ane areas of the critical and nozzle exit section
‘f and ГР.) for an assigned thrust known from thermal caiculation ma 2 и
of specific thrust P ana assigned or known loss factors 9,. and
i ,
с
Theoretical fuel consumption, i.e., neglecting losses
в“ (1.39)
ть
Real fuel consumption, i.e., taking losses into account, is necessary to ensure assigned thrust
И = >. (1.40)
From expressions (1.39) and (1.40) we obtain the relationship between real and theoretical expenditures of fuel:
G,=+, (1.41)
« [©
i.e., for production of assigned thrust it is necessary to pass more
fuel in order to compensate for losses.
Theoretical area of critical section f,,, is determined from к} Гогти1а (1.19)
G3 1 } =. (1.42) Real area cf critical section Са taking equations (1.32) and (1.41) into account ;
or Se aoe ae . (25643) р Ре
This means that the area of the critical section must be increased
Oniy in order to pass through it the additional fue} eonsumption
for compensating losses in the nozzle, this additional fuel eonsunption for compensation of losses in the chamber, not requiring an increase
in fe .
Let us define the area of nozzle section in a cut. According
tc the equation of expenditure theoretical Г and real f, wiil
accordingly be equal to
eee (1.44 Я: ) м. (1.45) Л» Жал: ть
Let us find the approximate connection between f to equation (1.30)
3 and f3- According
ит, (1.86)
On the basis of the equation of state
¥: RT, т; а: т (1.47)
24
en (Bhs reora(2)
then in accordance with equality (1.34) (1.48)
Putting in expression (1.45) the values G., 3: апа УЗ from 1
rs oO += a 64 м 2 ” fe tA — + . = ры w on funy . I> л ыы № 5 [97 — . i “J <
» taking into account
о 2 oi a be bus = . lm со <2 ‚ - © хх с ct А le >
бк _ Ine ah aha и. (1,39)
We see that the influen f icsse hows up on a sharper increase
in 73 вап 1т Г. . The cause of this is that the value of Рзи › р. :
besides the increase of expenditure, is influenced also by the
i decrease of real speed из as compared to w..
3
25
СНАРТЕР II NOZZLES OF A LIQUID FUEL ROCKET ENGIUIF
In the nozzle of the chamber of the en-ine there occurs expansion and acceleration of procucts of combustion, i.e., the transformation of thermal energy obtained in the combusticn chamber iuio kinetic energy of the motion of <ases. The quality and weight of tne whole propulsicn system depend on the quality of operation of tne nozzle, its economy and weizht.
2.1. Types of iiozzles and asic equirements of “her
At present there are used or there is investirated the possibility cf using; the following basic types of nozzles (Fiz. 2.1): conical, profilea and nozzles with a central bcdy.
nound nozzles
г)
с
.
Nozzles with a central body
d) e) Г) 5)
Fig. 2.1. Types of nozzles of the liquid-fuel rocket engine: a — conical; b -— profiled; ec — with an angular entrance; d ~— annular; e — with full external expansion; f - with partial inter- nal expansion; & ~- plate with free internal expansion.
Conical and Profiled 10221]ез
Conical nozzles have the supercritical section in the form of a cone with a direct generarix (lig. 2.la). They are the simplest to manufacture anu have been widely in rocket engines.
With respect to economy of the operation, 1.е., with respect to the inagnitude of losses, and weight characteristics, they yield to profiled nozzles and at present are almost completely displaced by them, finaing application only in certain engines of low thrust.
Profiled nozzles have the generarix of the supercritical section made in a curve, which coircldes with the streamline (Fig. 2.16, с). At present this is the most widespread type of nozzles of a liquid fuel rocket engine [ZhRD]. ‘There are nozzles with a smooth entrance into the supercritical section of the nozzle (Fig. 2.1b) and nozzles having а break of the reneratrix in the throat. The latter type of nozzle is called a nozzle with angular entrance into the supersonic section or, simply, nozzle with angular entrance (Fig. 2.1c).
Sometimes nozzles whose throat has the form of a circle, in contrast to nozzles with a central body, are called ordinary or
` 2
er ee
er at
в. —
round nozzles. But usually by conical or profiled nozzles round nozzles are implied.
Nozzles With a Central body
In recent years there has been intensively investigated thie possibility of the application in a 2Z2hRD of nozzles with a central body similar in principle to the type of nozzles successfully used in a jet engine [VRD].
Nere are the following types of nozzles with a central body.
Ring nozzles (Fig. 2.1d), the expansion of flow in which is limited by an annular channel with solid walls. In principle
the operation of annular nozzles does not differ from the operation of round nozzles.
jJozzles with full external expansion (Tig. 2.le), not having an external wall forming the flow after the throat. Frequently this type of nozzle Is simply called nozzle with a central body.
Nozzles with partial internal expansion (Fig. 2.1f) where the external wall determines expansion only up to a definite pressure.
Such type of nozzle is intermediate between nozzles shown on Fiz. 2.14 апа 2.1е. The application of these nozzles can appear expedient with the necessity of deep expansion and the acceleration of gas up to great M values.
Plate nozzles (see Fig. 2.1¢), thus called because of the plate form of the central body with a free internal surface of expansion, since after the critical section they do not have an internal wall.
Problem of the Designing of Nozzles and Requirements for Then.
From a thermal calculation of the engine there are known only dimensions of the throat of the nozzle fy, nozzle exit section
23
fy (or the pressure is assigned on nozzle P3)- In the designing
of the combustion chamber we also determine dimensions of the
entrance into the nozzle section. However, other important dimensions of the nozzle determining its form and design dimensions (in particular, the length of the nozzle and angles of inclination of walls of the nozzle in the entrance and outlet sections) are unknown to us.
The problem of designing the nozzle consists in the determination of such a contour of walls of the nozzle with which the following basic requirements for the nozzles would be satisfied.
1. The nozzle should have losses of thrust as small as
possible, i.e., as large a value of the coefficient of the nozzle Ф с 1s possible.
2. The surface of the walls of the nozzle at assigned fw and г should be the least, which decreases the weight of the nozzle and facilitates its cooling.
3. The construction and technology of manufacture of the nozzle should be as simple as possible.
As frequently happens in technology, the indicated requirements are to a certain degree contradictory, and the full satisfaction one of them leads to a certain impairment of other properties of the nozzle. Therefore, in the designing of the nozzle depending upon the assignment of the engine, we take a certain compromise solution.
2.2. Losses in the Nozzle of a Liquid Fuel Rocket Engine
Classification and Estimate of Losses
As was already indicated (see s@ction 1.3), losses in the nozzle of a liquid fuel rocket engine are estimated by the coefficient
29
Quantity Ф с depends on various kinds of losses in the nozzle, the basic of which are the following:
1. Losses to the dispersion of speed at the outlet of the п022]@ Фра.
2. Frictional losses of gas on walls of the по221е фр. 3. Losses at the entrance into the nozzle ax. 4, Losses to the nonequilibrium of the process of expansion Финер.
5. Losses connected with the nonadiabatic flow of products
of combustion along the nozzle. Sometimes they are called cooling losses Фолл.
6. Losses to the narrowing of the section of the flow Фе».
7. Losses taking place with the outflow of two-phase working substances @¢.
In certain cases losses in the nozzle are conditionally attributed to losses in thrust appearing due to the off-design nature of the operating conditions of the nozzle gap. This is inadmissible since losses of thrust due to the off-design nature of operating conditions do not depend on the quality of the flow of processes in the nozzle. However, sometimes in the comparative estimate of different contours of shortened nozzles, it is convenient to
_ consider these losses by introduction of the coefficient gq», referred to the nozzle.
Each of the indicated kinds of losses is estimated the appropriate coefficient @ (pac Gr,etc.) expressed as
30
P,— 4P,
= Р. (2.1)
упеге АР — decrease in thrust from a fiven type of loss. Knowin=
for every kind of los3 oy: we can determine %$с:
P
= oe ы 6 == ] — zr = в s -, =S('-$4)-w—n (2.2) =!
vaking Into account equation (2
tle
7 3
), WE will obtain
=> %—(n—1).
a (2.3)
It is nore convenient (and more usual) tc determine 4
*с not as the Sul $1 but as the product
Те FpecPrp Pen Paep PorsPeyn PQ: (2.4) The difference in the quantity 4
, determined by formulas (2.3) or (2.4) is small.
Accordins to results Of experinental d
ata, the total marpnitude ef losses in the nozzle is dete
riined by tie formula (1.36): Фе = Кал/Ка.
Let us examine the components of losses entering into expression (2.4),
Losses to the Dispersion of Орееч at the Outlet of the Nozsle
In deriving the equat
ion of thrus¢ ме с direction of the flow of ¢
onsidercd that the asses passing from the neazle is
a ie
i a
не.
in parallel to the axis of the nozzle. In reality, if in section fy the direction of the wall of the nozzle is not in parallel to the axis, then the velocity of the flow directed along the wall is deflected from the direction of the action of the tractive force (Fig. 2.2). The traction of the nozzle is determined only by the component of speed parallel to the axis Wee
Since
w<
DP; * const nas the for. of a sphere of padius р with surface Гу.
#16. 2.0. Determination of @pece
То determine the thrust let us Separate on surface fi the annular element with are 8 tncluucd between anples @ ana p+d6, and let us find tiie thrust of the clement. Tne axial component of the thrust of the element in a vacuum
ЧР... = =: we + P32nRB cos 8.
(2.5)
Considering, that
©, = ©, COs 3;
R mtn (2.6)
3108 Rak, sin’, ’
we fo
and suostitutine Cxpressions (2.4) treo eyuation (:.5), we wt cutain
€P ya on Bsn peont. d+ p,2n азс. ap.
Intesrating: this expression within llidis from o to Bay we obtrte wd
Pane (М ei sin cos B+ py sin сов В) ыы
% [= Geo) 4 пы (2.7) эм? В The flow rate threurh surface ft 6, 9 | чел. fr. зесоглапсе with equations (2.5) the surface of the elenent e .. г\ 5 = == — —ы ® (2.2 ве ла = 2лЮ aap = 2x ing. (een) and